Abstract:
The state-of-the-art of theories on dynamic seismic reliability of structures is systematically reviewed from three aspects: state variable models, basic variable models, and pragmatic simplified models. For the state variable models, using the random vibration theory, methodologies for random vibration analysis are classified into two categories: One is the statistical-characteristics oriented methods, which deal with the problems of evolution of statistical moments from the space of basic random variables into the space of the state variable; another is the probability-density oriented methods, which cope with the problems of evolution of probability density from the space of basic random variables into the space of the state variable. Two representative methods of the two categories, namely the statistical linearization approach and the probability density evolution method, are critically discussed. For the basic variable models, the methods for analysis of dynamic seismic reliability of structures that take into consideration the randomness in system parameters, and the theory and methods of transformation from the dynamic reliability problems into static ones, are summarized; then, a comparison analysis is made for the recently proposed methods, including the tail equivalence linearization method, the subset simulation, and the equivalent extreme events method. For the pragmatic simplified models, three methodologies are reviewed, including the direct approach based on stochastic ground motion simulation and deterministic time-history analysis, the simplified approach based on the uniform-hazard response spectrum and equivalent nonlinear systems, and the semi-analytical approach based on simplified analytical formulations of seismic reliability and numerical simulation. Finally, the problems existing in the recent global seismic reliability theories of structures are discussed and summarized. In addition, some suggestions are provided for input models of seismic actions, search of the main failure modes, failure criteria of structures, multiple properties of structural failure modes, and global limit state functions of structures.